Colors of
variables: wff
setvar class |
Syntax hints:
∈ wcel 2098 ∪ cun 3945
⊆ wss 3947 {csn 4630
0cc0 11144 ℕcn 12248
ℕ0cn0 12508
ℤcz 12594 |
This theorem was proved from axioms:
ax-mp 5 ax-1 6 ax-2 7
ax-3 8 ax-gen 1789 ax-4 1803 ax-5 1905
ax-6 1963 ax-7 2003 ax-8 2100
ax-9 2108 ax-10 2129 ax-11 2146 ax-12 2166 ax-ext 2698 ax-sep 5301 ax-nul 5308 ax-pr 5431 ax-un 7744 ax-1cn 11202 ax-icn 11203 ax-addcl 11204 ax-addrcl 11205 ax-mulcl 11206 ax-mulrcl 11207 ax-i2m1 11212 ax-1ne0 11213 ax-rnegex 11215 ax-rrecex 11216 ax-cnre 11217 |
This theorem depends on definitions:
df-bi 206 df-an 395
df-or 846 df-3or 1085 df-3an 1086 df-tru 1536 df-fal 1546 df-ex 1774 df-nf 1778 df-sb 2060 df-mo 2529 df-eu 2558 df-clab 2705 df-cleq 2719 df-clel 2805 df-nfc 2880 df-ne 2937 df-ral 3058 df-rex 3067 df-reu 3373 df-rab 3429 df-v 3473 df-sbc 3777 df-csb 3893 df-dif 3950 df-un 3952 df-in 3954 df-ss 3964 df-pss 3966 df-nul 4325 df-if 4531 df-pw 4606 df-sn 4631 df-pr 4633 df-op 4637 df-uni 4911 df-iun 5000 df-br 5151 df-opab 5213 df-mpt 5234 df-tr 5268 df-id 5578 df-eprel 5584 df-po 5592 df-so 5593 df-fr 5635 df-we 5637 df-xp 5686 df-rel 5687 df-cnv 5688 df-co 5689 df-dm 5690 df-rn 5691 df-res 5692 df-ima 5693 df-pred 6308 df-ord 6375 df-on 6376 df-lim 6377 df-suc 6378 df-iota 6503 df-fun 6553 df-fn 6554 df-f 6555 df-f1 6556 df-fo 6557 df-f1o 6558 df-fv 6559 df-ov 7427 df-om 7875 df-2nd 7998 df-frecs 8291 df-wrecs 8322 df-recs 8396 df-rdg 8435 df-neg 11483 df-nn 12249 df-n0 12509 df-z 12595 |
This theorem is referenced by: nn0z
12619 nn0zd
12620 nn0zi
12623 nn0ssq
12977 nthruz
16235 oddnn02np1
16330 evennn02n
16332 bitsf1ocnv
16424 pclem
16812 0ram
16994 0ram2
16995 0ramcl
16997 gexex
19813 iscmet3lem3
25236 plyeq0lem
26162 dgrlem
26181 2sqreultblem
27399 archirngz
32915 dffltz
42061 diophrw
42182 diophin
42195 diophun
42196 eq0rabdioph
42199 eqrabdioph
42200 rabdiophlem1
42224 diophren
42236 etransclem48
45672 |